Empirical modeling of the percent depth dose for megavoltage photon beams

Introduction This study presents an empirical method to model the high-energy photon beam percent depth dose (PDD) curve by using the home-generated buildup function and tail function (buildup-tail function) in radiation therapy. The modeling parameters n and μ of buildup-tail function can be used to characterize the Collimator Scatter Factor (Sc) either in a square field or in the different individual upper jaw and lower jaw setting separately for individual monitor unit check. Methods and materials The PDD curves for four high-energy photon beams were modeled by the buildup and tail function in this study. The buildup function was a quadratic function in the form of dd2+n with the main parameter of d (depth in water) and n, while the tail function was in the form of e−μd and was composed by an exponential function with the main parameter of d and μ. The PDD was the product of buildup and tail function, PDD = dd2+n·e−μd. The PDD of four-photon energies was characterized by the buildup-tail function by adjusting the parameters n and μ. The Sc of 6 MV and 10 MV can then be expressed simply by the modeling parameters n and μ. Results The main parameters n increases in buildup-tail function when photon energy increased. The physical meaning of the parameter n expresses the beam hardening of photon energy in PDD. The fitting results of parameters n in the buildup function are 0.17, 0.208, 0.495, 1.2 of four-photon energies, 4 MV, 6 MV, 10 MV, 18 MV, respectively. The parameter μ can be treated as attenuation coefficient in tail function and decreases when photon energy increased. The fitting results of parameters μ in the tail function are 0.065, 0.0515, 0.0458, 0.0422 of four-photon energies, 4 MV, 6 MV, 10 MV, 18 MV, respectively. The values of n and μ obtained from the fitted buildup-tail function were applied into an analytical formula of Sc = nE(S)0.63μE to get the collimator to scatter factor Sc for 6 and 10 MV photon beam, while nE, μE, S denotes n, μ at photon energy E of field size S, respectively. The calculated Sc were compared with the measured data and showed agreement at different field sizes to within ±1.5%. Conclusions We proposed a model incorporating a two-parameter formula which can improve the fitting accuracy to be better than 1.5% maximum error for describing the PDD in different photon energies used in clinical setting. This model can be used to parameterize the Sc factors for some clinical requirements. The modeling parameters n and μ can be used to predict the Sc in either square field or individual jaws opening asymmetrically for treatment monitor unit double-check in dose calculation. The technique developed in this study can also be used for systematic or random errors in the QA program, thus improves the clinical dose computation accuracy for patient treatment.

Rare-Earth Oxides as Alternative High-Energy Photon Protective Fillers in HDPE Composites: Theoretical Aspects

This work theoretically determined the high-energy photon shielding properties of high-density polyethylene (HDPE) composites containing rare-earth oxides, namely samarium oxide (Sm2O3), europium oxide (Eu2O3), and gadolinium oxide (Gd2O3), for potential use as lead-free X-ray-shielding and gamma-shielding materials using the XCOM software package. The considered properties were the mass attenuation coefficient (µm), linear attenuation coefficient (µ), half value layer (HVL), and lead equivalence (Pbeq) that were investigated at varying photon energies (0.001–5 MeV) and filler contents (0–60 wt.%). The results were in good agreement (less than 2% differences) with other available programs (Phy-X/PSD) and Monte Carlo particle transport simulation code, namely PHITS, which showed that the overall high-energy photon shielding abilities of the composites considerably increased with increasing rare-earth oxide contents but reduced with increasing photon energies. In particular, the Gd2O3/HDPE composites had the highest µm values at photon energies of 0.1, 0.5, and 5 MeV, due to having the highest atomic number (Z). Furthermore, the Pbeq determination of the composites within the X-ray energy ranges indicated that the 10 mm thick samples with filler contents of 40 wt.% and 50 wt.% had Pbeq values greater than the minimum requirements for shielding materials used in general diagnostic X-ray rooms and computerized tomography rooms, which required Pbeq values of at least 1.0 and 1.5 mmPb, respectively. In addition, the comparisons of µm, µ, and HVL among the rare-earth oxide/HDPE composites investigated in this work and other lead-free X-ray shielding composites revealed that the materials developed in this work exhibited comparable X-ray shielding properties in comparison with that of the latter, implying great potential to be used as effective X-ray shielding materials in actual applications.

Theoretical Determination of High-Energy Photon Attenuation and Recommended Protective Filler Contents for Flexible and Enhanced Dimensionally Stable Wood/NR and NR Composites

This work aimed to theoretically determine the high-energy-photon-shielding properties of flexible wood/natural rubber (NR) and NR composites containing photon protective fillers, namely Pb, Bi2O3, or Bi2S3, using XCOM. The properties investigated were the mass attenuation coefficient (µm), linear attenuation coefficient (µ), and half value layer (HVL) of the composites, determined at varying photon energies of 0.001–5 MeV and varying filler contents of 0–1000 parts per hundred parts of rubber by weight (phr). The simulated results, which were in good agreement with previously reported experimental values (average difference was 5.3%), indicated that overall shielding properties increased with increasing filler contents but decreased with increasing incident photon energies. The results implied the potential of bismuth compounds, especially Bi2O3, to replace effective but highly toxic Pb as a safer high-energy-photon protective filler, evidenced by just a slight reduction in µm values compared with Pb fillers at the same filler content and photon energy. Furthermore, the results suggested that the addition of 20 phr wood particles, primarily aimed to enhance the rigidity and dimensional stability of Pb/NR, Bi2O3/NR, and Bi2S3/NR composites, did not greatly reduce shielding abilities; hence, they could be used as dimensional reinforcers for NR composites. Lastly, this work also reported the optimum Pb, Bi2O3, or Bi2S3 contents in NR and wood/NR composites at photon energies of 0.1, 0.5, 1, and 5 MeV, with 316–624 phr of filler being the recommended contents, of which the values depended on filler type and photon energy of interest.